Question

What is the volume of the cylinder below?

Answer 1

now, let's recall Cavalieri's Principle, "solids with equal altitudes and cross-sectional areas at each height, have the same volume".

so, even though this cylinder is slanted, it has the same cross-sectional area as a cylinder that's straight-up, whose altitude is h = 5, and radius r = 4.

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} h=5\\ r=4 \end{cases}\implies V=\pi (4)^2(5)\implies V=80\pi$